Adaptive H8 Fuzzy Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Adaptive H8 Fuzzy Control for a Class of Uncertain Discrete-Time Nonlinear Systems

Tsung-Chih Lin (Feng-Chia University, Taiwan) and Shuo-Wen Chang (Feng-Chia University, Taiwan)
Copyright: © 2010 |Pages: 20
DOI: 10.4018/jalr.2010100104

Abstract

In this paper, an adaptive interval type-2 fuzzy controller is proposed for a class of unknown nonlinear discrete-time systems with training data corrupted by noise or rule uncertainties involving external disturbances. Adaptive interval type-2 fuzzy control scheme and control approach are incorporated to implement the main objective of controlling the plant to track a reference trajectory. The Laypunov stability theorem has been used to testify the asymptotic stability of the whole system and the free parameters of the adaptive fuzzy controller can be tuned on-line by an output feedback control law and adaptive laws. The overall adaptive scheme guarantees the global stability of the resulting closed-loop system in the sense that all signals involved are uniformly bounded. The simulation example is given to confirm validity and tracking performance of the advocated design methodology.
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Introduction

The fuzzy controllers provide a systematic and efficient framework to incorporate linguistic fuzzy information from human expert (Wang 1993, 1994; Wang & Mendal, 1992; Buckley, 1992). Furthermore, fuzzy control is a model free approach, i.e., it does not require a mathematical model of the system under control. Control engineers are now facing more and more complex systems, and the mathematical models of these systems are more and more difficult to obtain. Thus, in control engineering, model free approaches become more important. There are some model free approaches in conventional control, such as nonlinear adaptive control and PID control. Fuzzy control gives another model free approach (Hwang & Lin, 1992; Wang, Liu, et al., 2002; Wang, Lin, et al., 2002; Lin, Wang, et al., 2004; Chen, Lee, et al., 1996; Leu, Lee, et al., 1999).

In the last two decades, optimal control theory has been well developed and found extensive application to efficiently treat the robust stabilization and disturbance rejection problems (Lin, Wang, et al., 2004; Wang, Liu, et al., 2002; Wang, Lin, et al., 2002). In the conventional optimal control, the plant model must be known beforehand. In this study, the optimal control design will be extended toward the nonlinear systems with unknown or uncertain models via fuzzy technique. However, several adaptive fuzzy sliding mode control systems have been developed for continuous-time systems (Chang, Park, et al., 2002; Lee, Kim, et al., 2001; Yu, Man, et al., 1998; Utkin, 1977), which cannot be expanded into discrete-time systems directly. Only a few of them are devoted to discrete-time systems (Shi, 2007; Sarpturk, Istefanopulos, et al., 1987; Han, Su, et al., 2000; Shaocheng & Tianyou, 1998; Fuchun, Zengqi, et al., 1998; Guo, Shi, et al., 2009; Spooner, Ordonez, et al., 1997a, 1997b).

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